Hi there, i was doing a paper, and i came across a question, i have tried it, but i don't know where to start from ;(
Please help me!
I have attached the question down below.
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Dec 09, 2020 5:08 pm
22 Replies
Dec 09, 2020 8:22 pm
To answer this question, I would do the following
1. Find out the area of the small hexagon in terms of x. To do this, basically make triangles from the centre of the hexagon, to each vertex. Then, work out the area of one of the triangles using 1/2 x base x height and times it by how many triangles were in the hexagon. [Note: to work out the area of the small triangle, you're gonna need to do SOH CAH TOA].
2. Once you got the area of the small hexagon in terms of x, times it by p^2 to get the area of the large hexagon. (Remember, if the length scale factor is p, the area scale factor is p^2). Once you times it by p^2, take away your two areas and factorise - you'll end up with what they've given you.
Spoiler
My solution, look at it after trying it yourself
Dec 09, 2020 10:29 pm
@zeeshan Thanks so much for the response, i have another question to ask, but I can't upload the question onto here. Do you have any email or social media? Its very urgent.
Dec 09, 2020 11:18 pm
Dec 10, 2020 3:42 pm
@zeeshan Oh ok, i have a few more questions that i am stuck with, is it ok if you can help me?
Dec 10, 2020 3:48 pm
Dec 10, 2020 10:23 pm
This is how you should approach these ratio questions. Make x or y the subject of the equation they’ve given you, then plug in a value for x and y. Have a look at the example below
if you have a quadratic and it says make a ratio from it, make one side equal 0, factorise it, make each bracket = 0 and do the same thing as above.
Spoiler
Solution to the part (b) if you’re still stuck
For the circle theorem question, use the alternate segment theorem. The angle x is equal to the angle I put an arrow next to. Try to work out that angle using the theorems you know, then x is the same thing.
For the mean question, approach it like the following:
For the lower bound question, break it down using other triangles in the cube:
Mar 23, 2021 9:16 pm
@zeeshan Hi I was looking through your working out for the ratio solving question (part b), and I noticed that there might have been a mistake.
3x would have to multiply with 2x to get 6x^2 and that would change the answer at the end, although I'm not sure if I am correct.
Here is my attempt to go further but I got 2 y values and now I'm confused... :/
Thanks
Mar 23, 2021 9:58 pm
Yes, your factorisation is correct. (2x - 5y)(3x + 4y)
The reason you didnt get a negative value was just a small mistake right at the end
When you make y the subject, you wouldve divided both sides by -4, so y = -3/4.
Well done though!
Just out of curiosity, how did you find this thread?
Mar 23, 2021 10:05 pm
@zeeshan Ohh, yeah I get the question now, thanks. So would the end ratio at the end be
x:y
3:2
[since the y fraction would be 2/5]
And I got this question from one of my previous tests, and I was confused about this one so I found this thread online.
Mar 23, 2021 10:21 pm
When you let x = 1, y = 2/5
So x : y is 1 : 2/5
or if you times both sides, then x : y = 5 : 2
Mar 23, 2021 10:25 pm
Mar 23, 2021 10:33 pm
Mar 29, 2021 7:15 pm
Mar 30, 2021 11:09 pm
Part a, the new triangles should look like this
for the “single transformation”, I would say it’s a reflection by a scale factor of -1, from centre point (2.5, -1)
for part b, an invariant point is a point that doesn’t change after the transformation, the only point that would stay the same after an enlargement with scale factor -1 at the point (2.5, -1) is the point (2.5, -1).
Mar 28, 2021 11:36 pm
@zeeshan sorry to bother you but would you be able to further explain the answer to the cube question please
Mar 30, 2021 11:31 pm
Jun 26, 2022 10:06 am
@zeeshan hi, would you know what topic this would fall under? so i could practise it. thanks.
Mar 24, 2021 4:21 pm
Hi, by any chance do you know what the paper is called? i did this for my test and was curious about other questions but don’t have it online to share!
Mar 25, 2021 9:47 am
Unfortunately I got no idea where these papers are from ?
If someone knows, that would be nice though. Seems like some hard questions were in the paper.
Mar 30, 2021 11:34 pm
Mar 29, 2021 12:01 am
could someone explain how to answer the circle question please
Mar 30, 2021 11:31 pm
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